Allow your darlings to be murdered / Knowing when to let an NPC go

There's a decision that shapes a GM, one that separates the men from the boys, the wheat from the chaff, the good from the bad.
You've put in time and effort creating a Non-Player Character for your game. You've not just statted them, you've woven them into the very fabric of your game world. They have a name, a back story, concerns, interests, a personality, goals, hopes and fears.
This is a recurring antagonist. A nemesis. Someone who your players love to lock horns with, who they curse in the day and ally with in darkest need.
Then the players just kill them. Usually in a summary fashion that in no way hints to the greatness of this character.

What do you do? Let the character die? Move on? Start again?
Or snatch them from the jaws of death, resurrect them off screen or retcon their survival?

This is the test.

I recently had to make this decision, twice, in my weekly Night's Black Agents game.

I created the first actual vampire the players were to meet, who was supposed to thrash them within an inch of their lives before dying himself or fleeing or driving them off.
They pretty much cut his head off in the first round of combat with him, dropping him instantly.
OK. That's fine. He has healing powers and is supposed to be hard to kill and fucking scary. Fair enough. Let them have their victory.
Their surveillance cameras picked him up walking around and killing Mafia henchmen with his bare hands some ten, fifteen minutes later. That put the wind up them.

The next time they meet him, some four sessions later, they were sufficiently wary of his recuperative abilities to nuke the site from orbit. They wheeled a bomb disposal robot, packed to the rafters with C4, into the building he was in and remotely detonated it.

I spent the next week agonising over what to do.
He was a vampire with supernatural speed, reflexes, resilience and healing. Of anyone could have survived, it would be him.
But that would be a spit in the face to the players. They'd put everything they had into making sure that they killed this guy dead. It would be unsatisfying to deprive them off that kill.
But what about the narrative function that the NPC was supposed to serve? And what about all the effort I put into building him?

Let me tell you a story.
Back in the late 90s I played in a Vampire: the Dark Ages game. I was playing a 7th Gen Brujah based on the Crusader Tancred de Hautville, who was a lot of a bastard. One of the other players was a 7th Gen Tremere who specialised in the Thaumaturgical Path of Fear. This becomes important shortly.
For some reason we were fighting a horde of flesh eating zombies in a tunnel network beneath London. It turned out that the source of all of these
Undead was a Celestial Chorus mage (don't ask me why, I still don't know to this day). He told us to stop killing the zombies, or he'd have to stop us.
So we attacked.
Our tried and tested tactic was for the Tremere to use the Path of Fear, which reduced the targets dice pools by a sizable amount, often preventing them from acting, and then the rest of us would beat the shit out of them.
So, the Tremere used Path of Fear and rolled well, reducing the Mage's dice pool by 9 dice. This pretty much guaranteed his death. The rest of us surged forward.
At this point the Storyteller starts panicking and tells us that the Mage is teleporting out of the tunnels.
Well, this is patently impossible, not unless the Mage has an Arête score of 10 (Arête is the measure of a Mage's magical might. A score of 3 let's you throw fireballs. A score of 10 literally makes you an actual God), which is highly improbable.
But the Storyteller informs us that, yes, the Mage is a God and can create a fully functioning universe in 6 days or less.
He rolls his one dice, gets a success and has the Mage escape.
Fucking atrocious! 

To this day I find this deeply unsatisfying. I'm getting that empty, gnawing, hollow feeling in my stomach just thinking about it.
If only I could roll back time and punch the storyteller in the gut and shout "how d'ya like them apples?!"

Back to Night's Black Agents...
Should the vampire escape?
No.
They found his severed arm in the rubble of the building, and the rest of him stuck in a collapsed bolt hole in the cellar.
Their play paid off. They get the rewards. My NPC gets to be interrogated, and if they're sloppy he may escape (sans arm). He'll probably die. That's fine.